Security is likely to be intensified for some time
Several Kashmiri militant groups fighting for independence from India have denied responsibility for the attack.
Some Indian politicians have demanded that action be taken against Pakistan should the attack have been the work of the militants.
India says they receive logistical support from Pakistan. The two countries have fought two wars over Kashmir.
'Senseless violence'
Neighbouring Sri Lanka and Nepal, both with their own insurgency problems, denounced the attackers.
"We in Sri Lanka strongly condemn such senseless violence directed at elected representatives of the people of India," the new Sri Lankan Prime Minister Ranil Wickramasinghe said.
Tamil Tiger rebels in Sri Lanka carried out attacks on Wednesday that resulted in the deaths of 25 people.
King Gyanendra of Nepal, who declared a state of emergency to fight Maoist rebels three weeks ago, described the attack in Delhi as "heinous".
"All the nations of the world should come together to end and fight against terrorism," the king said.
The American embassy in Delhi in a statement offered "our deepest sympathy to the families of the victims of this attack".
The French embassy firmly condemned and denounced "the murderous terrorist attack".
Strength and resilience
British Prime Minister Tony Blair said India would recover.
"Indian democracy has shown its strength and resilience over the years, and I am confident it will do so again despite this appalling attack, Mr Blair said in a statement.
And the European Union's External Affairs Commissioner, Chris Patten said he was "appalled" by the attack.
"We feel particular sympathy for India - the largest democracy in the world - over this attack on its elected parliament," Mr Patten said in a statement issued in Brussels.